Chemical
Quantities
Unit 6
Chapter 10, Section 10.1
The Mole: A Measurement of Matter
Objectives
 When you complete this presentation, you will be able
to:
 describe methods of measuring the amount of
something.
 define Avogadro’s number, N0, as it relates to a mole
of a substance.
 distinguish between the atomic mass of an element and
its molar mass.
 describe how the mass of a mole of compound is
calculated.
Measuring Matter
 We live in a world of quantities, of measurement.
 What was your grade on the 1st Semester Exam?
 How many friends do you have on Facebook?
 How big is a “tall” cup of coffee at Starbucks?
 Chemists have similar kinds of quantitative questions.
 How many kg of iron can we get from 100 kg of ore?
 How many grams of N2(g) and H2(g) must be combined
to give us 200 g of NH3(g)?
 What volume of CO2(g) is produced when we burn one
gallon of gasoline?
Measuring Matter
 To solve chemists’ problems we need to measure the
amount of matter we have.
 What do we mean by the “amount” of matter?
 For chemists, this is not a trivial question.
Measuring Matter
 When we measure matter, do we mean …
 the number of atoms or molecules?
 How many oxygen molecules combine with each
methane molecule when we burn natural gas?
 the mass of the elements or compounds?
 How many grams of oxygen (as O2 gas) combines with
ten grams of methane (as CH4 gas) when we burn natural
gas?
 the volumes of the matter?
 How many liters of oxygen (as O2 gas) combines with one
liter of methane (as CH4 gas) when we burn natural gas?
Measuring Matter
 Some units for measuring indicate a specific number
of items.
 A pair always means two.
 A dozen always means twelve.
Measuring Matter
 For example, apples are measured in three different
ways.
 At a fruit stand, they may be sold by the count (3 for
$2.40).
 In a supermarket, you buy apples by the weight
($1.29/lb) or mass ($2.79/kg).
 At an orchard, you buy apples by the volume
($12.00/bushel).
Measuring Matter
 For example, apples are measured in three different
ways.
 At a fruit stand, they may be sold by the count (3 for
$2.40).
 In a supermarket, you buy apples by the weight
($1.29/lb) or mass ($2.79/kg).
 At an orchard, you buy apples by the volume
($12.00/bushel).
 Each of these may be equated to a dozen apples.
Measuring Matter
 For example, apples are measured in three different
ways.
 At a fruit stand, they may be sold by the count (3 for
$2.40).
 By count: 1 dozen apples = 12 apples
Measuring Matter
 For example, apples are measured in three different
ways.
 At a fruit stand, they may be sold by the count (3 for
$2.40).
 By count: 1 dozen apples = 12 apples
 In a supermarket, you buy apples by the weight
($1.29/lb).
 By mass: 1dozen apples = 2.0 kg apples
Measuring Matter
 For example, apples are measured in three different
ways.
 At a fruit stand, they may be sold by the count (3 for
$2.40).
 By count: 1 dozen apples = 12 apples
 In a supermarket, you buy apples by the weight
($1.29/lb).
 By mass: 1dozen apples = 2.0 kg apples
 At an orchard, you buy apples by the volume
($12.00/bushel).
 By volume: 1dozen apples = 0.20 bushel apples
Measuring Matter
 Knowing how the count, mass, and volume of apples
relates to a dozen apples allows us to convert between
these units.
 For example, we could calculate the mass of …
 a bushel of apples or
 90 average sized apples
 … by using the following conversion factors
1 dozen apples
12 apples
2.0 kg apples
1 dozen apples
1 dozen apples
0.20 bushel apples
Sample Problem 10.1
What is the mass of 90 average-sized apples if 1 dozen
apples has a mass of 2.0 kg?
Known:
Unknown:
# of apples = 90 apples
mass of 90 apples = ? kg
12 apples = 1 dozen apples
1 dozen apples = 2.0 kg apples
Process:
# of apples → dozens of apples → mass of apples
mass of 90 apples = 90 apples ×
1 dozen apples
12 apples
×
2.0 kg apples
1 dozen apples
Sample Problem 10.1
What is the mass of 90 average-sized apples if 1 dozen
apples has a mass of 2.0 kg?
Known:
Unknown:
# of apples = 90 apples
mass of 90 apples = ? kg
12 apples = 1 dozen apples
1 dozen apples = 2.0 kg apples
Process:
# of apples → dozens of apples → mass of apples
mass of 90 apples =
90 × 1 × 2.0
12 × 1
kg apples = 15 kg apples
What is a Mole?
 Counting things as big as apples is a reasonable way to
measure the amount of something.
 Would counting the grains of sand on a beach be a
reasonable way to measure the amount of sand?
 Would counting individual atoms in a kilogram of a
compound be a reasonable way to measure the
amount of matter?
What is a Mole?
 Counting individual small things (such as atoms or
molecules) can be difficult.
 It is much easier if the things are grouped into
convenient units.
 Counting individual eggs could be tedious.
 Unless they are grouped by dozens.
What is a Mole?
 Chemists use a similar kind of unit to measure
amounts of matter (atoms and molecules).
 The unit for the amount of matter is a mole,
abbreviated as mol.
 1 mole of any thing is defined as 6.02 × 1024 pieces of
that thing.
 That is 6,020,000,000,000,000,000,000,000 pieces.
 This number is called Avogadro’s number, N0.
What is a Mole?
 Just to be sure you understand this …
 1 mol of hydrogen atoms is 6.02 × 1024 atoms
 1 mol of hydrogen molecules is 6.02 × 1024 molecules
 1 mol of glucose molecules is 6.02 × 1024 molecules
 1 mol of pencils is 6.02 × 1024 pencils
 1 mol of students is 6.02 × 1024 students
 1 mol of grains of sand is 6.02 × 1024 grains
 There are only 7.005 × 1020 grains of sand on earth.
 1 mol of stars is 6.02 × 1024 stars
 There are only 9 × 1021 stars in our universe.
What is a Mole?
 Let’s look at a couple of compounds a little more
closely.
 1 mole of hydrogen molecules is 6.02 × 1023 molecules.
 Each hydrogen molecule, H2, is composed of two
atoms of hydrogen.
 That means there are 2 × 6.02 × 1023 = 12.04 × 1023
hydrogen atoms in 1 mole of hydrogen molecules.
What is a Mole?
 Let’s look at a couple of compounds a little more
closely.
 1 mole of glucose molecules is 6.02 × 1023 molecules.
 Each glucose molecule, C6H12O6, is composed of 6
atoms of carbon, 12 atoms of hydrogen, and 6 atoms
of oxygen
 That means there are 6 × 6.02 × 1023 = 36.12 × 1023
carbon atoms in 1 mole of glucose molecules.
 That means there are 12 × 6.02 × 1023 = 72.24 × 1023
hydrogen atoms in 1 mole of glucose molecules.
 That means there are 6 × 6.02 × 1023 = 36.12 × 1023
oxygen atoms in 1 mole of glucose molecules.
What is a Mole?
 Let’s practice converting from number of particles to
number of mols.
 The conversion looks like this:
# of moles = # of representative particles ×
1 mole
6.02 × 1023 representative particles
 Let’s try Sample Problem 10.2 (page 291).
Sample Problem 10.2
 Magnesium is a light metal used in the manufacture of
aircraft, automobile wheels, tools, and garden
furniture. How many moles of magnesium is
1.25 × 1023 atoms of magnesium?
Known:
Unknown:
# of atoms = 1.25 × 1023 atoms
mols = ? mol Mg
1 mol Mg = 6.02 × 1023 atoms Mg
Process:
atoms → mols
# of moles = # of representative particles ×
1 mole
6.02 × 1023 representative particles
Sample Problem 10.2
 Magnesium is a light metal used in the manufacture of
aircraft, automobile wheels, tools, and garden
furniture. How many moles of magnesium is
1.25 × 1023 atoms of magnesium?
Known:
Unknown:
# of atoms = 1.25 × 1023 atoms
mols = ? mol Mg
1 mol Mg = 6.02 × 1023 atoms Mg
Process:
atoms → mols
# of moles = 1.25 ×
1023
atoms Mg ×
1 mole Mg
6.02 × 1023 atoms Mg
Sample Problem 10.2
 Magnesium is a light metal used in the manufacture of
aircraft, automobile wheels, tools, and garden
furniture. How many moles of magnesium is
1.25 × 1023 atoms of magnesium?
Known:
Unknown:
# of atoms = 1.25 × 1023 atoms
mols = ? mol Mg
1 mol Mg = 6.02 × 1023 atoms Mg
Process:
atoms → mols
# of moles =
1.25 × 1023 × 1
6.02 × 1023
moles Mg = 0.208 moles Mg
What is a Mole?
 Let’s practice converting from number of mols to
number of particles .
 The conversion looks like this:
# of particles = # of mols ×
6.02 × 1023 representative particles
1 mol
 Let’s try Sample Problem 10.3 (page 292).
Sample Problem 10.3
 Propane gas is used for cooking and heating. How
many atoms are in 2.12 mol of propane (C3H8)?
Known:
# of mols = 2.12 mols
1 mol C3H8 = 6.02 × 1023 molecules C3H8
1 molecule C3H8 = 11 atoms (3 C + 8 H)
Unknowns:
# atoms = ? atoms
Process:
mols → molecules → atoms
# of atoms = # of mols ×
6.02 × 1023 molecules
1 mol
×
# of atoms
1 molecule
Sample Problem 10.3
 Propane gas is used for cooking and heating. How
many atoms are in 2.12 mol of propane (C3H8)?
Known:
# of mols = 2.12 mols
1 mol C3H8 = 6.02 × 1023 molecules C3H8
1 molecule C3H8 = 11 atoms (3 C + 8 H)
Unknowns:
# atoms = ? atoms
Process:
mols → molecules → atoms
# of atoms = 2.12 mols ×
6.02 × 1023 molecules
1 mol
×
11 atoms
1 molecule
Sample Problem 10.3
 Propane gas is used for cooking and heating. How
many atoms are in 2.12 mol of propane (C3H8)?
Known:
# of mols = 2.12 mols
1 mol C3H8 = 6.02 × 1023 molecules C3H8
1 molecule C3H8 = 11 atoms (3 C + 8 H)
Unknowns:
# atoms = ? atoms
Process:
mols → molecules → atoms
# of atoms =
2.12 × 6.02 × 1023 × 11
1×1
atoms = 1.40 × 1025 atoms
The Mass of a Mole
 What is so special about Avogadro’s Number?
 Why do we use “6.02 × 1023” any way?
The Mass of a Mole
 If we measure out 6.02 × 1023 atoms of an element,
the mass is equal to the atomic mass of that element.
 For 6.02 × 1023 atoms of H, mass = 1.01 g
 For 6.02 × 1023 atoms of C, mass = 12.01 g
 For 6.02 × 1023 atoms of O, mass = 16.00 g
 If we measure out 6.02 × 1023 molecules of a
compound, the mass is equal to the molar mass of
that compound.
 For 6.02 × 1023 molecules of CO2, mass = 44.01 g
 For 6.02 × 1023 molecules of C6H12O6, mass = 180.16 g
The Mass of a Mole
 The atomic mass of an element is the mass of 1 mol
of that element.
 The molar mass of a compound is the mass of 1 mol
of that compound.
The Mass of a Mole
 To calculate the molar mass of a compound
 find the number of grams of each element in one mole
of the compound
 add the masses of the elements in the compound
 For example:
 for glucose, C6H12O6:
 mass of C = 6 × 12.01 g = 72.06 g
 mass of H = 12 × 1.00794 g = 12.09528 g
 mass of O = 6 × 16.00 g = 96.00 g
 mass of C6H12O6 = (72.06 + 12.10 + 96.00) g = 180.16 g
The Mass of a Mole
 To calculate the molar mass of a compound
 find the number of grams of each element in one mole
of the compound
 add the masses of the elements in the compound
 For example:
 for water, H2O:
 mass of H = 2 × 1.00794 g = 2.01588 g
 mass of O = 1 × 16.00 g = 16.00 g
 mass of H2O = (12.02 + 16.00) g = 18.02 g
The Mass of a Mole
 To calculate the molar mass of a compound
 find the number of grams of each element in one mole
of the compound
 add the masses of the elements in the compound
 For example:
 for methane, CH4:
 mass of C = 1 × 12.01 g = 12.01 g
 mass of H = 4 × 1.00794 g = 4.03177 g
 mass of CH4 = (12.01 + 4.03) g = 16.04 g
The Mass of a Mole
 Try some on your own: find the molar mass of …
NH3
17.02 g/mol
CO2
44.01 g/mol
NaCl
58.44 g/mol
H2SO4
98.08 g/mol
KOH
56.11 g/mol
Fe2O3
159.69 g/mol
Summary
 When chemists measure matter, they measure …
 the numbers of atoms or molecules
 the mass of the elements or compounds
 the volumes of the matter
 The unit for the amount of matter is a mole.
 1 mole of any thing is defined as 6.02 × 1023 pieces of
that thing.
 This number is called Avogadro’s Number, N0.
Summary
 To convert from numbers of particles to number of
mols, we use the conversion…
# of moles = # of representative particles ×
1 mole
6.02 × 1023 representative particles
 To convert form number of mols to number of
particles, we use the conversion …
# of particles = # of mols ×
6.02 × 1023 representative particles
1 mol
Summary
 The atomic mass of an element is the mass of 1 mol
of that element.
 The molar mass of a compound is the mass of 1 mol
of that compound.
 To calculate the molar mass of a compound find the
number of grams of each element in one mole of the
compound and add the masses of the elements in the
compound.